Prisoner's dilemma

From Lesswrongwiki

The Prisoner's dilemma is a classic problem in game theory. Two players independently have the option of cooperating with or defecting against the other player. If both players cooperate, they each receive a payoff C from a third party (a "banker" or benevolent nature); if they each defect, they both receive payoff D; if one cooperates and one defects, the defector receives payoff T and the cooperator receives payoff S. The prisoner's dilemma is the situation in which T > C > D > S. The payoffs are assumed to be in utils, each player only wants to maximize her own payoff, without any regard in either direction for the other player.

Notice that if you treat the other player's decision as completely independent from yours, if the other player defects, then you score higher if you defect as well, whereas if the other player cooperates, you do better by defecting. So it would seem that the rational decision would be to defect (at least if the game is to be played only once), and indeed, this is what classical causal decision theory says. And yet—and yet, if only somehow both players could agree to cooperate, they would both do better than if they both defected. If the players are timeless decision agents, they can.